Solve A=(x+3)(x-3)-x(x-3)

$$A = ( x + 3 ) ( x - 3 ) - x ( x - 3 )$$

Solve for A

$$A=3\left(x-3\right)$$

Solution Steps

Consider \left(x+3\right)\left(x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$A=x^{2}-9-x\left(x-3\right)$$

Use the distributive property to multiply x by x-3.

$$A=x^{2}-9-\left(x^{2}-3x\right)$$

To find the opposite of x^{2}-3x, find the opposite of each term.

$$A=x^{2}-9-x^{2}+3x$$

Combine x^{2} and -x^{2} to get 0.

$$A=-9+3x$$

Solve for x

$$x=\frac{A+9}{3}$$

Steps for Solving Linear Equation

Consider \left(x+3\right)\left(x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$A=x^{2}-9-x\left(x-3\right)$$

Use the distributive property to multiply x by x-3.

$$A=x^{2}-9-\left(x^{2}-3x\right)$$

To find the opposite of x^{2}-3x, find the opposite of each term.

$$A=x^{2}-9-x^{2}+3x$$

Combine x^{2} and -x^{2} to get 0.

$$A=-9+3x$$

Swap sides so that all variable terms are on the left hand side.

$$-9+3x=A$$

Add 9 to both sides.

$$3x=A+9$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{A+9}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{A+9}{3}$$

Divide A+9 by 3.

$$x=\frac{A}{3}+3$$